 ### 1. Introduction

Trapezoidal footing is a type of footing that carries unequal loads from 2 columns when the heaviest load outside the column distance is limited.

It is used when the area of footing is fixed and the soils at the site are loose soil.

### 2. Formula for Calculating Trapezoidal Footing Volume

As we know that, Trapezoidal footing is made by the superimposing of a rectangular cuboid and truncated pyramid as shown in the figure below.

Now,

The volume of trapezoidal footing=Volume of Rectangular cuboid (V1)  +  Volume of a truncated pyramid (V2)

= V1 + V2       …………….(Eq.1)

I. Volume of rectangular cuboid (V1);

= A * B * hc    …………….(Eq.2 )

where,

A= length of the cuboid

hc= Height of cuboid

II. Volume of truncated pyramid ( V2 );

= ht/3 * ( A1 + A2 + √(A1 +A2) )  ……..(eq.3)

Where,

A1= area of a bottom surface of the truncated pyramid

A2= area of the upper surface of the pyramid

ht= height of the pyramid

From equation 1,2 and 3 we can write the final  formula for calculating volume of  trapezoidal footing as shown below;

= V1 + V2

= ( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) )

Now ,We are going to find out the volume of trapezoidal footing shown in figure 3 as above;

i. ht=300mm = 0.3m

ii. hc=300mm=0.3m ( lets assume)

iii. Area of cuboid (A *B)= (2000mm * 1600mm) = 3.2 m²

iv. Area of bottom surface of the pyramid(A1) =3.2m²

v. Area of top surface of the pyramid (A2)= (800*800)mm^2=0.64m²

Now, Total Volume= V1 + V2

=( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) )

=(3.2 * 0.3) + 0.3/3 (3.2+0.64 +(√(3.2+0.64)))

=0.96 +0.57995

= 1.539959 m^3

The total volume of the trapezoidal footing of figure 3 = 1.5399m^3

### 3. Uses

Trapezoidal footing is use

I. For residential house and building.

II. When load applied is uneven or unequal.

III. The soil at the site is loose.

a. Concrete uses are less.

b. Cheap to construct.

c. Less reinforcement is needed.

a. Good for small buildings only.

b. Chance of settlement.

c. Foundation subjected to pull out, torsion, moment.